The sources for pre-7th century battles lacks any detail and even sources of the 7th and 6th centuries BC are only sporadic so we can only guess.

The Neo Assyrians seem to have used cavalry as early as the 9th century BC in number, whereas cavalry didn't seem to be introduced into China until the 5th century BC. It's not until the late 8th century however, that cavalry seem to have gained a clear prominence over chariots. In this, the Assyrian armies (and many other Near Eastern armies) should be more mobile than the contemporary Chinese armies. However, the role of cavalry was not as aggressive as it would be in the 4th century BC where they would charge right into enemy formation. Tactically, the early cavalry usually only charged after missile fire weakened the enemy formation and they played a secondary role to the infantry (most of which were archers).
There are virtually no records in detail of how the Assyrian infantry fought, but if they were at all like the later Persian army, which were also prominently archers, then their formation is probably less sophisticated than those of China's. The Persian infantry were mostly archers and lacked compact formations and that's why they often got bested by the Greek hoplites, which maintained cohesive defensive formation.

The deployment of the Persian infantry usually consisted of a line of spearmen holding large shields at the front protecting a number of archers and missile troops behind. That is not to say that the Persian spearmen were not well armoured soldiers, who were highly skilled in individual combat. Persian spearmen, just as their Assyrian counterparts, were very able close-quarter warriors. However, very rarely were they required to fight in a close formation. Each soldier fought independently in the melee protecting his section of the shield wall supported by the archers and light infantry behind him. At the battle of Mycale Herodotus states (9.102), The Persians, as long as their line of shields remained intact, successfully repelled all attacks and had by no means the worst of things;...They [the Athenians] burst through the line of shields and fell upon the enemy in a mass assault. For a time, indeed, the assault was held, but in the end the Persians were forced to retreat within the protection of the barricade.The Persians were very able individual warriors at close quarters, especially protected behind their shield wall, but against an organized and disciplined mass of well-armoured heavy infantry their shortcomings could beexposed.Theconcept of individual heroism permeated the Persian military society. Nobles strived to excel at fighting as individuals with the bow, javelin and spear. The Immortals, an elite Persian unit of infantry, were well armed individuals who could fight effectively as archers or spearmen in close quarters. But they did not fight in any tactical formation...According to Herodotus, there is no differentiation between units and all Persians, that is all ethnically Persian soldiers, were armed in the same way. (CALGARY 2012)

Chinese infantry formations on the other hand, seem to be much more complex than even contemporary Greek hoplites and even adopted equal arms in proportion:

"Greek kill mechanisms were simple specifically because the form of the target, the enemy phalanx, was always constant and unchanging. Chinese kill mechanisms were much more complex because the disposition of the enemy always played a major role in determining how that enemy should be targeted. This relational aspect, not present in Greek warfare, greatly complicated the strategic situation, placing the onus on strategists to out-think their opponents rather than merely overwhelming them with direct force. Direct force was rarely adequate for achieving victory, since the goal became to understand the disposition of the enemy and be able to exploit it while concealing your true disposition from the enemy. This goal, when reduced to its lowest terms, is really a relatively simple optimization problem."

When the Greeks were struggling to escape the confining nature of the phalanx and its single tactic of the mass collision, China had already perfected numerous formations and methods of deployment, as well as an underlying hierarchical organization based upon the squad of five that, when coupled with precise training methods, allowed articulation, segmentation, and the execution of both orthodox and unorthodox tactics. -The Essence of War: Leadership and Strategy from the Chinese Military Classics, Ralph D. Sawyer p.1 Intro

However, this only pertains to the 6th century BC and after, details of battles in early China are rare, this is probably the earliest account; the battle of Cheng Pu in 632 BC.
The Qin center army consisted of two sections: the main infantry force making up the majority of the center army, and an elite force, Duke Wen's bodyguards, called the "first army," attached to the right flank of the main part of the center army. Qin attacked first, beginning with an advance of both left and right armies. The Qin left engaged first, smashing the Ch'u right army in an attack that was "urgent, impetuous, and rapidly successful" . The Qin right army then served as a "holding force, fixing the Ch'u center and preventing it from attacking the Qin center or aiding the Ch'u left wing". The Ch'u center could not move, since doing so would invite a flank attack from Qin left. While this was happening, Qin right was also advancing. They advanced to a predetermined spot, within bowshot range, and quickly reversed, feigning flight. The Ch'u left took the bait and pursued. Before the battle, tree branches had been pre-placed in front of the Qin right antly at the point where they turned and feigned flight. As the Ch'u left army made its way towards these branches and the fleeing Qin right, the Qin chariots swept across the front, dragging the tree branches. This dragging action caused dust to rise, obscuring the "fleeing" Qin right army, who, behind the veil of dust, was presumably circling out left with plans to take Ch'u's flank. The chariots did not engage the advancing Ch'u left army. Instead, as they approached, Qin's "first army," the Duke's elite unit, broke from the center and swept into the Ch'u left army flank. At this precise moment, the Qin right army who had feigned flight appeared at the scene to rout the Ch'u left army .
Thus, while exact force structures are not given, we can glean from the story that the major force structure themes were utilized. As for the Qin army, they were highly mobile-they were able to execute an effective feint involving a mass infantry force, as well as several sweeping and flanking maneuvers. Qin used combined arms in a most ingenious way as part of a ruse de guerre. Interestingly, as suggested by the theorists, the chariots played only a supporting role and did not engage infantry forces. The Qin forces must have been able to transition quickly between formations-the feigning maneuver and subsequent circling and attack demonstrates this. We also know from the Tso chuan and Shih Chi accounts that rigid hierarchies were in place and largely responsible for the effectiveness of the Qin army in routing Ch'u. On the other hand, the Ch'u army seemed rigid in their formations and their strategy. The Ch'u center stood its ground while an entire third ofthe Ch'u army was smashed.

The battle shows the state of Jin already had flexible formational changes, while the state of Chu were still relatively rigid in formation (but at least they had a cohesive formation). It also seem that infantry did not fight separately from chariot in China until the late 7th century BC. The Assyrians also used iron, whereas the Zhou used bronze, but unless some studies provide HV levels and qualitative comparison between the two, early iron is not necessarily superior to good bronze, especially when furnace temperature in China was the highest in the world, and by 600 BC, were already making bimetallic blades that were harder than iron.
In sum, Near Eastern armies had a lead in mobility because of their adoption of cavalry, whereas Chinese infantries tend to have more sophisticated and flexible infantry formations and had a more variety of arms (halberds, spear, crossbows, and bows). If Chinese armies before the 7th century BC were not like they were later, then Assyrian probably had a slight edge in quality at the time (especially considering it had infantries operating independently from chariots, and can fight in more variety of terrains). It's hard to say which army in the 7th century had the edge. After the 7th century BC however, given that infantry archers seem to still be the primary Near Eastern arm, I would give the lead to Chinese armies by then because even in the Near East, infantries were more decisive than cavalries. In the 4th century BC, cavalries became more aggressive and overtook infantry as the more decisive unit, and both the Persian and Macedonian cavalry would head on charge into missile firing and infantry formation without the need for missiles to soften them up, but by then Chinese infantries had more powerful crossbows with complex trigger mechanisms that often blasted off direct frontal heavy cavalry charges (and cavalry also became a unit in China itself).

It's not clear when the crossbow was introduced in warfare. The Rites of Zhou (Zhou Li) mentioned trigger mechanism already, and the earliest excavated bronze trigger dates to the early 6th century BC in Shang Dong in the state of Lu. However, these early crossbows probably weren't as powerful as crossbows from the 4th century BC onwards, for we do not hear them standing out as much in earlier records. Cavalry might also have been first introduced to China in the state of Qin under Duke Qin Mu as early as the mid 7th century BC. For in 636 BC, we hear from Han Feizi that “The Duke (Mu), used 500 chariot, 2000 cavalry and 50,000 infantry to accompany Zhong Er to the Jin and make him the sovereign of Jin.”公( 秦穆公 )因起卒,革车五百乘,畴骑二千,步卒五万,辅 重耳 入之于 晋 ,立为 晋君。 The Lushi Chunqiu also mentioned cavalry with chariots shortly afterwards when Duke Jinwen (Zhong Er) attacked Ye. "The duke of Jin attacked Ye, and rewarded the returning generals. Zhao Ai said: 'does the lord give out reward at the beginning or at the end? If the lord gives out rewards at the end, the cavalrymen and charioteers will survive.' " Cavalry and chariots were already separate units by this time.

However, both the Han Feizi and Lushi Chunqiu dates to the 3rd century BC, yet it makes sense that the Qin would have cavalry, as it was the first state which interacted heavily with the Western Rong, when Qin Mugong conquered them.

The Guanzi, a text probably composed in the 4th century BC attributed to Guanzhong of the state of Qi in the 7th century BC, already talked about "Qikou" or "cavalry bandits" among the Rong, or western barbarians. It is hardly surprising for China to have adopted cavalry from them at any time after this date.

How did the population of the Jin decline so much compared to the Han? Is the Three Kingdom phase kill that much people?

The three kingdom population might have declined to as much as just 25 million, the population might have recovered to around 38 million by the height of western Jin (See Ge Jianxiong). The Eastern Jin only had southern China, so its population should be less than half of that.

I have no idea that the Zhou is that strong. How about the Shang though?

I think the use of mass produced crossbow must be like the introduction of firearms, equalizing the battlefield and putting down of elite warrior class. I notice that while much is written about the usage of crossbow in China, there are few I know on how it was invented and why it was adopted to such extent compared to other civilization.

The Opium War show how far Western miilitary progress, it is certainly not the biggest disparity in equipment or overall military power.

I know that if the distance are reduced, the Chinese regimes probably have the military advantage over Europe in most of history.

What do you think the point for the biggest disparity in equipment and individual quality of an Asian power compared to European ones?

At what period that a reverse Opium War is possible?

My current opinion in quality disparity would be the late Tang to Five Dynasties Ten Kingdom, there is a Chinese painting showing crossbow with stirrups, fully armored horse, full body laminar armor and what looks like a hand cannon. Chinese armor also seems to be more sophisticated at this time compared to Song Dynasty.

I also heard very impressive units being used at this period like 10 floor ships with flamethrower and elephants.

The Western Zhou bureaucracy has been studied in more detail recently by Li Feng and we are starting to understand its structure. It was far more centralized than Medieval European feudalism (in that the regional states are more similar to "subject officials" rather than "vassals" of medieval kings; the later implying a reciprocal legal obligation from the king, whereas the Zhou king had no such obligation and his will is the law); the more decentralized spring and autumn period which followed is closer to European feudalism. I see Western Zhou imperial control more similar to the Achaemenid or early Sassanian Empires and was a world empire in its own right (the Eastern Zhou might have had an even larger population than Achaemenid Persia, but its not as centralized by then). From my limited understanding, the regional state (guo) in the Zhou Empire often played similar role to the satrap in the Sassanian Empire.

1) Both were usually hereditary (although it seems to be more the case with the Guo)
2) These satraps, like the guo, were not equal in status. In the Sassanian Empire, we have Shahs and Shahrdar ruling the satraps whereas in the Zhou, we have a five degree hiearchical nobility system of Gong, Hou, Bo, Zi, Nan for the guo (regional states).
3) Both contain imperial inspectors to check local power, in the Sassanid Empire we have the Shahrab whereas in the Zhou, we have the Jian监.
4) The Sassanian Marzban and the Zhou Jianguo 监国; seem like parallel positions. Both are mini hereditary polities that the conquest regime established strategically alongside the conquered. So Marzbans are typically established along frontiers like Khurasan, whereas we also have the famous 三监; or "three jians" established by the Zhou around Henan to oversee the remnants of Shang power (we also have evidence from the oracle bones that Jianguo was already a Shang institution).
5) Both contains "client kingdoms" which already existed before the central authority came to power. In Sassanian's case, we have states like Albania and in the Zhou, we have the state of Chu.

Therefore, the Zhou was hardly a loose feudal state, but more similar in central control to later Persian Empires. It's just that the Zhou centralization is still less bureaucratic than the Qin and later dynasties, but compare well with most other pre-modern polities. There are no such detailed study of the Shang so far, but it might well be similar to the Western Zhou.

What do you think the point for the biggest disparity in equipment and individual quality of an Asian power compared to European ones?

At what period that a reverse Opium War is possible?

My current opinion in quality disparity would be the late Tang to Five Dynasties Ten Kingdom, there is a Chinese painting showing crossbow with stirrups, fully armored horse, full body laminar armor and what looks like a hand cannon. Chinese armor also seems to be more sophisticated at this time compared to Song Dynasty.

I also heard very impressive units being used at this period like 10 floor ships with flamethrower and elephants.

Probably between the 4th-early 7th century. This is the period where stirrup and fully armored heavy cataphracts became the main striking arm in warfare, and we have no such equivalent until the 10th century Byzantines in the west (when armor weight reached at least 70 lb and horses became fully armored too). The early Parthian cataphract had lighter armor, no stirrup, and only made up around 1/10 of the entire cavalry force and was not the prominent arm in combat. Early Byzantine and Sassanian cavalry also had thin armor and usually only the front of the horse was armored. Metal stirrup was only introduced to Europe in the late 6th century, and probably into the Middle east in the middle of the 7th century, and to India in the 10th century. Northern and Southern dynasties also still used long powerstroke crossbows, so the infantry had an advantage as well. In siege the trebuchet was also not introduced into the west until the late 6th century.
The next largest disparity would probably be the 2nd century BC-1st century AD. Not only did the Han army have a lead in missile in the form of crossbows, but its metallurgy was explicitly noted to be superior to states of the western region, a lead which we do not find in later sources.

Probably between the 4th-early 7th century. This is the period where stirrup and fully armored heavy cataphracts became the main striking arm in warfare, and we have no such equivalent until the 10th century Byzantines in the west (when armor weight reached at least 70 lb and horses became fully armored too). The early Parthian cataphract had lighter armor, no stirrup, and only made up around 1/10 of the entire cavalry force and was not the prominent arm in combat. Early Byzantine and Sassanian cavalry also had thin armor and usually only the front of the horse was armored. Metal stirrup was only introduced to Europe in the late 6th century, and probably into the Middle east in the middle of the 7th century, and to India in the 10th century. Northern and Southern dynasties also still used long powerstroke crossbows, so the infantry had an advantage as well. In siege the trebuchet was also not introduced into the west until the late 6th century.
The next largest disparity would probably be the 2nd century BC-1st century AD. Not only did the Han army have a lead in missile in the form of crossbows, but its metallurgy was explicitly noted to be superior to states of the western region, a lead which we do not find in later sources.

In the period of 4th-7th century, can an Asian force win with numerical disparity like the British did in Opium War?

While the Tang have a clear advantage, I know less about other non-China East Eurasian power like the Tibetan Empire, how do they compare to Roman and Sassanid Empire? I heard all of their infantry are heavily armored and they give the Tang a hard fight until the end.

How do Kofun Japan or the Korean Three Kingdoms compare to Germanic kingdoms? or the Tarim Basin? It seems that the period really have a lot of different powers appearing in East Eurasia.

I know the Sassanid and Roman armor are thin, but at least they still cover the whole body of the rider, the period from the fall of the Sassanid to the 12th century show almost no heavy armor in Western Eurasia, except for Byzantine cataphract, which is why I think that late tang and Five Dynasties would have more advantage than the 4th-7th century.

Stirrup while already used in the West, it always depicted with some wearing stirrups and other don't, which show it probably was not universally used until late 11th century.

Also is the disparity of the early Song and Jin Dynasty bigger than Han and Tang Dynasty?

Early Near Eastern cavalries of the Parthians (as well as early Sassanian) and the Sogdian cavalry did seem to have full armored horses. Parthian cataphracts:

However, they seem to lack the shock power of later heavy cataphracts with stirrups and have trouble even punching through Roman infantry formations. This is probably because of two things. The armor of the early cataphracts was extremely thin and hence light. The scale found at Dura Europo was only 0.25 mm, and most armors of the time were no more than 0.8 mm. Second, without stirrup, the melee fighting done after the initial collision would be limited, this also puts a limit to the number of cataphracts as well.
However, later Sassanian cataphract seem to only have the front half of the horse covered and the main 5,000 Clibanarii force of the early Byzantine only had a Chamfron to protect the head.

How do Kofun Japan or the Korean Three Kingdoms compare to Germanic kingdoms? or the Tarim Basin? It seems that the period really have a lot of different powers appearing in East Eurasia.

Koguryo, together with the Yan had some of the earliest depiction of double metal stirrup and later on also have crossbow units. It had 3-4 million people and a recorded army of around 300,000 (not clear whether this is the standing army or the mobilization potential, but even the later makes it a significant power); so it should be at least a comparable power to the Sassanian Empire or the Hunnic Empire in the 5th century, and far stronger than the Germanic kingdoms.

I know the Sassanid and Roman armor are thin, but at least they still cover the whole body of the rider, the period from the fall of the Sassanid to the 12th century show almost no heavy armor in Western Eurasia, except for Byzantine cataphract, which is why I think that late tang and Five Dynasties would have more advantage than the 4th-7th century.

Technologically, I don't think the Song and Jin lead was as large as the lead from 2nd century BC-7th century. Other than metallurgy, armament, and heavy cavalry catching up and being heavier, Western Eurasia essentially attained trebuchet and also counterweight trebuchet (having different strengths compared to East Asian siege technology). Tactics is a different matter, and considering the lack of samples of battle in earlier periods, I don't think we can conclude anything beyond paper comparisons.

There is a lot more to just technology in warfare. As Tonio Andrade pointed out, much of the reason for late Qing losses has even more to do with weaker command structure than with equipment. The PLA's technological gap with the UN forces in the Korean war was probably even more significant than the Qing equipment was compared to the British or Japanese in the 19th century, but it was still able to push back and then stalemate the UN forces with just roughly 4:1 numerical superiority, largely because command structure and experience of the PLA was much greater than armies of the late Qing and ROC (this is even more true of navies; the gap between the Beiyang fleet and IJN was minimal in 1894; the gap between the Chinese and Japanese navy in the 1990s was much larger in favor of the Japanese). The largest technological gap between the East and the "West" might have been in the 1980s-1990s, when the United States developed tanks and planes that were 2-3 generations ahead and attained ground, aerial, and naval joint operation capabilities tied with satellite, scaring the PRC to invest heavily in military technology as well.

I also think much of the superiority of Eastern Eurasian nomads over western nomads is due to superior state organization and command structure more than technology. This even influence bow design. Much of the Seljuk bows used against the crusaders couldn't penetrate crusader armor (whereas Mongol bows could), not because longer ear power bows weren't around (the Magyars introduced them to Europe long ago), but because much of the cavalrymen were temporarily conscripted pastoralists using their private hunting bows; whereas large empires of the east could better standardize and regulate bows to only heavier long ear war bows for war.

There are some modern picture that supposedly show Sassanid cataphract as fully armored. These picture show Sassanid cataphract fighting Arabs in 7th century.

However I noticed that currently there is no contemporary depiction showing the Sassanid wearing lamellar over mail.

You are saying early period Byzantine clibanarii, what's the difference with cataphract?

I searched in Google, this is what I found

How is the 10th century cataphract than the one before?

About the Song and Jin period,

I found this in Wikipedia, a quote taken from Andrade from History of Jin

"The heaven-shaking-thunder bomb is an iron vessel filled with gunpowder. When lighted with fire and shot off, it goes off like a crash of thunder that can be heard for a hundred li [thirty miles], burning an expanse of land more than half a mu [所爇圍半畝之上, a mu is a sixth of an acre], and the fire can even penetrate iron armor."

What happen if that is used against a Western style castle? Could it compensate in power against counterweight trebuchet?

Also what make European cavalry in the early Jurchen Jin heavier than previous century? Couched lance was used in Central Asia before that. Their horse is still unarmored and full mail body armor only start being used widely after 1150.

While overall European armor increase in coverage, Chinese armor also cover in that period than during early Tang and Song crossbow are stronger as well.

I think China is in better position after Self Strengthening Movement to adopt modern technology.

While at the end of WW 2 and 1940s, the US and Soviet Union have nukes and bombers, the PRC at least have factories and modern guns.

About Western and Eastern nomads, in the 4th century BC to 4th century AD maybe the Western nomads have superior armor.

Past 4th century, Eastern nomads have full body armor and full horse armor, superior number, superior organization and mobility. How they obtained so much metal for armor and weapons? Most of the time from what I see they would have superior equipment Western European sedentary tribes.

The 13th century Seljuk armor is not comparable to even the earliest illustrated Ilkhanate equipment in early 14th century.

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